Proposals of probability measuressuitable for acconting data based bankruptcy models

Abstract

Financial distress and bankruptcy modeling represents large and important field of economic research topics. This paper concerns with general structure of score oriented models in form of linear or affine forms built upon data available from standard accounting reports. For illustration purposes, we present well-known models, i.e. Altman, Neumaier, Ohlson, and Zmijewski one. However, the paper is focused mainly to probabilistic framework, which is getting more actual attention in practice for company financial health quantitative analysis, now. At first, the logit and probit transformations used for Ohlson, and Zmijewski model, respectively, are presented, as well as one model for calculation of probability of company default based upon Z-score values. Our contribution to this field is presented in the central part of the paper. We assume the score value to be an outcome of a random variable, which is introduced by its cumulative distribution function. This function is constructed systematically as a piecewise smooth function collected from three branches. Two of them, there are tail functions, belong to exponencial family. Whereas the central branch is specified as a linear function. At each joint, which is related to model grey zone bound, point smoothness of two adjacent branches is maintained by specific boundary conditions applied. Several cumulative distribution functions are presented,together with their probability density functions. Next, we select a SME ranked company, and apply the proposed technique to company survival analysis, as well as an analysis of company default probabilities. All calculations were performed by sw Mathematica.

Keywords

• Bankruptcy models
• Default probability
• Probability distributions
• Score oriented models
• Survival probability